ABSTRACT
A comprehensive study concerning the phase formation mechanism and growth/dissolution kinetics of sodium tungsten bronze crystals during the electrolysis of a 0.8Na2WO4-0.2WO3 melt was carried out. The regularities of deposit formation on a Pt(111) working electrode were investigated experimentally using cyclic voltammetry, chronoamperometry, scanning electron microscopy, and X-ray diffraction analysis. Models have been developed to calculate the current response during the formation, growth and dissolution of a two-phase deposit consisting of NaxWO3 and metallic tungsten or two oxide tungsten bronzes with different sodium content. These models consider mass transfer to the electrode and nuclei; chemical and electrochemical reactions with the participation of polytungstate ions, Na+, Na0, and O2-; as well as the ohmic drop effect. The approach was proposed to describe the dissolution of an NaxWO3 crystal with a nonuniform sodium distribution. The fitting of cyclic voltammograms was performed using the Levenberg-Marquardt algorithm. The NaxWO3 formation/growth/dissolution mechanism was determined. Concentration profiles and diffusion coefficients of [WnO3n]-, reaction rate constants, number density of nuclei, and time dependencies of crystal size were calculated. The proposed approaches and models can be used in other systems for the cyclic voltammogram analysis and study of the mechanism and kinetics of electrode processes complicated by phase formation; parallel and sequential electrochemical and chemical reactions; as well as the formation of a deposit characterized by a nonuniform phase and/or chemical composition.
ABSTRACT
The problem of diffusion-controlled growth following an instantaneous nucleation event was studied within the framework of a new numerical model, considering the spatial distribution of hemispherical nuclei on the electrode surface and the mutual influence of growing nuclei via the collision of 3D diffusion fields. The simulation of the diffusion-controlled growth of hexagonal and random ensembles was performed at the overpotential-dependent number density of nuclei. The diffusion flow to each nucleus within a random ensemble was simulated by the finite difference method using the derived analytical expressions for the surface areas and the volumes formed at the intersection of 3D diffusion fields with the side faces of a virtual right prism with a Voronoi polygon base. The implementation of this approach provides an accurate calculation of concentration profiles, time dependences of the size of nuclei, and current transients. The results, including total current density transients, growth exponents, and nucleus size distribution, were compared with models developed within the concept of planar diffusion zones, the mean-field approximation and the Brownian dynamics simulation method, as well as with experimental data from the literature. The prospects of the model for studying the initial stages of electrocrystallization were discussed.
ABSTRACT
Processes of nucleation and growth largely determine the structure and properties of thin films obtained by electrodeposition on foreign substrates. Theoretical aspects of the initial stages of electrochemical phase formation under constant and variable overpotentials are considered in this work. Simulation of multiple nucleation with mixed (charge transfer, and diffusion) controlled growth was performed for three cases (cyclic voltammetry, potentiostatic electrodeposition, and galvanostatic electrodeposition). The influence of the bulk concentration of depositing ions and the exchange current density at the electrolyte/nucleus interface on cyclic voltammograms (CVs), transients of current and overpotential, as well as the number and size of non-interacting new-phase nuclei was analyzed. It is found that, under galvanostatic conditions, the number of nuclei decreases as the concentration of depositing ions increases due to a more rapid decrease in overpotential. The proposed model was applied to determine the diffusion coefficient, exchange current density, and transfer coefficient considering the experimental CV.
